Restricted three body problem considering the perturbations of both oblate massive primaries

Abstract

This paper was conducted to investigate the periodic solution of the Perturbed Circular Restricted Three Body Problem (P-CRTBP) orbit with respect to the perturbations effect of the both oblate massive primaries. The governing equations of the satellite motion in this problem has been extracted employing Lagrangian mechanics. Since, the problem may have no closed-formed solution and the numerical methods must be utilized to address this type of issue, so the problem could have different periodic or non-periodic solutions depending on the initial conditions. For this purpose, an algorithm named “orbital correction algorithm” has been utilized to achieve the appropriate initial conditions of the P-CRTBP periodic orbit state variables. Since, the number of periodic solutions is restricted; the suitable initial guess vector as the inputs of the orbit correction algorithm increases the probability of achieving more accurate initial conditions. Suitable initial guess could be selected from the third-order approximation of the Unperturbed Circular Restricted Three Body Problem’s (U-CRTBP) equations of motion. Considering the effect of these synthetic perturbations, could be considered as a stepping stone to describe the spacecraft's natural motion in such problems. Since, the number of periodic solutions is restricted; the suitable initial guess vector as the inputs of the orbit correction algorithm increases the chances of achieving more accurate initial conditions.